The raised-cosine filter is a filter frequently used for pulse-shaping in digital modulation due to its ability to minimise intersymbol interference (ISI). Its name stems from the fact that the non-zero portion of the frequency spectrum of its simplest form (β = 1) is a cosine function, 'raised' up to sit above the f (horizontal) axis.
The raised-cosine filter is an implementation of a low-pass Nyquist filter, i.e., one that has the property of vestigial symmetry. This means that its spectrum exhibits odd symmetry about , where T is the symbol-period of the communications system.
Its frequency-domain description is a piecewise function, given by:
and characterised by two values; β, the roll-off factor, and T, the reciprocal of the symbol-rate.
The raised-cosine filter is an implementation of a low-pass Nyquist filter, i.e., one that has the property of vestigial symmetry. This means that its spectrum exhibits odd symmetry about , where T is the symbol-period of the communications system.
Its frequency-domain description is a piecewise function, given by:
 |
| The impulse response of such a filter is given by: |
and characterised by two values; β, the roll-off factor, and T, the reciprocal of the symbol-rate.
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